How to find all the equivalent matrices of a matrix in R?

Asked Apr 27 '15 at 15:35

Active Apr 27 '15 at 16:30

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I want to find all the equivalent matrices of a matrix, let's say it as M, but I want these equivalent matrices to have exactly the same diagonal elements with M and the same non-diagonal elements with M.

For example if M is

> M<-matrix(x,4,4);M
     [,1] [,2] [,3] [,4]
[1,]   22   -2   -2    2
[2,]   -2   22    2    2
[3,]   -2    2   22   -2
[4,]    2    2   -2   22

I want one of the equivalent matrix to be for example

     [,1] [,2] [,3] [,4]
[1,]   22    2   -2    2
[2,]    2   22    2   -2
[3,]   -2    2   22   -2
[4,]    2   -2   -2   22

As you can see not only M,but also all the equivalent matrices must be symmetric (M=transpose(M)).

I have tried lots of ways, such as "permut" and "Matrix" packages, but I can't find something to help me. I have used LU and QR decomposition, but it's not what I want.

Is there something to do with this problem???

Thank you all!

edited Apr 27 '15 at 16:30

asked Apr 27 '15 at 15:35

Vassilis Chasiotis

It seems you want `diag(s)*M*diag(s)` where `s[k] in {-1,+1}`. – Lutz Lehmann Apr 27 '15 at 16:03
To clarify: you don't care (other than symmetry) how the lower diagonal elements are arranged, just that the two matrices have the same collection? If that's the case, you might find (shameless plug) `vecsets` package helpful in verifying that the contents of the lower triangles are the same. – Carl Witthoft Apr 27 '15 at 16:03
LutzL, I want something like that. So, I want M=P*M1*P', where M1 is equivalent to M and P is a permutation matrix. – Vassilis Chasiotis Apr 27 '15 at 16:12
Carl Witthoft, I am gonna see the `vecsets`! Thanks for it! – Vassilis Chasiotis Apr 27 '15 at 16:14
Carl Witthoft, `vecsets` doesn't work! Thanks for it! – Vassilis Chasiotis Apr 27 '15 at 16:38
The answer is `rmperm {sna}`. – Vassilis Chasiotis Apr 27 '15 at 17:13
Vassilis: good that you found something which works. For reference, the way to write a function and its package is `sna:rmperm` , the way you'd call it from the command line. – Carl Witthoft Apr 28 '15 at 12:03

How to find all the equivalent matrices of a matrix in R?

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